Chelsea have announced they have completed the permanent signing of Mateo Kovacic from Real Madrid in a deal worth £40.3 million.

Kovacic's registration remained with Chelsea until June 30 after his season-long loan spell, meaning they could sign him from Madrid without breaching the two-window transfer ban handed down by FIFA in February and upheld in May.

"Real Madrid and Chelsea have agreed the transfer of the player Mateo Kovacic," the La Liga side said in a statement. "The club wishes to thank Kovacic for these years of commitment, professionalism and exemplary behaviour, and wishes him good luck in his next step."

His arrival bolsters Chelsea's midfield options in the absence of Ruben Loftus-Cheek, who will miss at least the first half of the new season after rupturing his Achilles' tendon during a postseason friendly against New England Revolution.

Kovacic enjoyed mixed fortunes during his loan spell at Stamford Bridge, displaying a good range of passing and close control but registering no goals and just two assists from midfield across all competitions.

Selling the Croatia international also enables Real Madrid to recoup some of the money they paid Chelsea to sign Eden Hazard, who swapped Stamford Bridge for Bernabeu earlier this month in a deal worth up to £130m.

Kovacic wanted to return to Chelsea on a permanent deal despite the departure of Maurizio Sarri after just one season to take over at Juventus, with Frank Lampard expected to be formally announced as his successor this week.